HONG KONG, Nov 2 (Reuters) - Chinese stocks rose on Friday on hopes of a wind-down in trade tensions after U.S. President Donald Trump said he had a “very good” phone conversation with Xi Jinping and that trade talks with the country were “moving along nicely”. ** At midday, the Shanghai Composite index was up 31.42 points or 1.21 percent at 2,637.65 while the blue-chip CSI 300 index was up by 1.9 pct. ** CSI300’s financial sector sub-index was higher by 0.98 percent and the consumer staples sector was up 3.19 percent while the real estate index was down 0.85 percent and the healthcare sub-index was firmer by 3.43 percent. ** The smaller Shenzhen index was up 2.08 percent and the start-up board ChiNext Composite index was higher by 3.34 percent. ** On Thursday night, U.S. President Donald Trump said he had a “very good” phone conversation with Xi while the Chinese state media reported that Xi wants stable relationship with the U.S. ** “If the trade war calms down, sentiments will improve across the market,” said Steven Leung, director of sales for UOB Kay Hian in Hong Kong. ** The phone conversation, which came ahead of the two leaders’ meeting in Argentina at the G-20 summit later this month, sent the yuan to the stronger side of 6.91 per dollar in the offshore market, a level not seen since October 11. ** In Hong Kong, the Hang Seng Index gained 2.40 percent to touch 26,026.18 while the index for Chinese H-shares listed in Hong Kong climbed 2.28 percent. Both the indexes jumped more than 2 percent in early trade. ** Around the region, MSCI’s Asia ex-Japan stock index was firmer by 1.55 percent while Japan’s Nikkei index was up 0.65 percent. ** While an easing of trade tensions helped lift stocks in Greater China, investors in the mainland were mostly reacting to Xi’s vow of support, through tax cuts and financial aid, for domestic private enterprises on Thursday night, said Zhang Qi, an analyst at Haitong Securities in Shanghai. ** “This is part of a series of encouragements coming through from the government,” he said, referring to the policy support announced by regulators, such as an improvement in market liquidity, earlier this week. ** “We have had a lot of negative headlines for a long time, with the trade war going on and the renminbi weakening,” he said. With both these factors turning around, “confidence is on the rise in China.” ** At midday, the onshore yuan was quoted at 6.9303 per U.S. dollar, 0.15 percent weaker than the previous close of 6.9199. ** The largest percentage gainers in the main Shanghai Composite index were Weifang Yaxing Chemical Co Ltd, up 10.1 percent, followed by Chunghsin Technology Group Co Ltd , up 10.05 percent and Hubei Mailyard Share Co Ltd , up 10.02 percent. ** The top gainers among H-shares were Air China Ltd, up 9.83 percent, followed by CSPC Pharmaceutical Group Ltd , up 7.77 percent and Tencent Holdings Ltd, up 6.55 percent. ** Tencent announced that it plans to expand into services such as healthcare, in a bid to grow its consumer business. ** The company’s shares jumped to its three-week high on Friday, contributing to the 6.2 percent rise in the sub-index of the Hang Seng index tracking the IT sector. ** By lunchtime, China’s A-shares were trading at a premium of 20.2 percent over the Hong Kong-listed H-shares. ** The top gainer on Hang Seng was Sino Biopharmaceutical Ltd , up 9.62 percent, while the biggest loser was PetroChina Co Ltd, down 1.38 percent.